An often-neglected portion of the radial drift is shown to drive an outward flux of co-current momentum when free energy is transferred from the electrostatic potential to ion parallel flows. This symmetry breaking is fully nonlinear, not quasilinear, necessitated simply by free-energy balance in parameter regimes for which significant energy is dissipated via ion parallel flows. The resulting rotation peaking is counter-current and has a scaling and order of magnitude that are comparable with experimental observations. The residual stress becomes inactive when frequencies are much higher than the ion transit frequency, which may explain the observed relation of density peaking and counter-current rotation peaking in the core.